"We have opened the door to training pilots and this with several other European countries who are also ready," he told TV station TF1. "I think discussions are under way with the Americans.
"The training can start from now."
After months of stalemate, Ukraine has been preparing to retake ground captured by Russia and is shoring up military assistance to help make its troops more battle-ready.
Mr Zelenskyy has for months been pleading for modern fighter jets such as the US-designed F-16, but Nato members have so far drawn the line at sending any such planes.
One French official close to air force command in February said that France could in theory send 13 recently decommissioned Mirage 2000-C fighters, but that it would probably take too long to train Ukrainian pilots to fly them.
Mr Macron and Mr Zelenskyy had dinner on Sunday night, as the Ukrainian leader visited several European countries to boost his weapons stockpile.
Ukraine and Russia conflict latest - in pictures
"In the coming weeks, France will train and equip several battalions with tens of armoured vehicles and light tanks including AMX-10RC," they said in a joint statement afterwards.
Mr Macron later refused to provide more details.
"We have decided to deliver more ammunition," he said.
France also decided to help "train their troops, the battalions that will be in charge of the counter-offensive", and "repair vehicles and cannon".
"France still has the same position: to help Ukraine resist," Mr Macron said. "A lot is at stake right now, because the success of this counter-offensive will be decisive for the capacity to build lasting peace."